Function spaces as path spaces of Feller processes

Let {X-t}(t greater than or equal to 0) be a Feller process with infinitesi mal generator (A, D(A)). If the test functions are contained in D(A), -A/C- c(infinity)(R-n) is a pseudo- differential operator p(x, D) with symbol p(x , xi). We investigate local and global regularity properties of the sample paths t --> X-t in terms of (weighted) Besov B-pq(s) (R, rho) and Triebel - Lizorkin F-pq(s) (R, rho) spaces. The parameters for these spaces are dete rmined by certain indices that describe the asymptotic behaviour of the sym bol p(x, xi). Our results improve previous papers on LEVY [5, 9] and Feller processes [22].